Schwarz-Christoffel analysis of polygonal linear material objects

In this short note, we explain a complex-analytic numerical algorithm using the Schwarz-Christoffel mapping, for estimating the fields in physical objects of a linear material with polygonal boundary and finite constitutive parameter inside an applied field, by numerically solving the corresponding matching conditions. Examples of such linear materials are linear magnetic or dielectric materials and conductive materials. The formalism of linear magnetic problems is used to develop the methodology.